Big Idea:
In this lesson, students are introduced to a real-life application of the Pythagorean Theorem and must use it to justify their decisions.

For today's Warm Up problems, I included two questions as review from previous days' concepts. The first problem will require students to apply the Pythagorean Theorem to determine the distance (length) between two points on a coordinate grid.

The second problem asks students to critique the thinking of others (MP 3) by deciding if they agree with Mia that the given dimensions are, indeed, those of a right triangle. If students disagree (which they should if they have applied the Pythagorean Theorem correctly) they should explain why.

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Today's lesson, The Taco Cart, is stolen from Dan Meyer, who has created and shared his amazingly creative "three-act lessons". This particular lesson launches in Act I with Dan setting the scene: He and his friend are at the beach and spot a taco cart up the road. His friend decides to walk directly to the cart, but Dan, believing that he walks much slower on sand than on the road, decides to walk straight to the road and then down the road to the cart. The students must decide (using mathematical evidence) who reaches the cart first.

Just as in Dan's other Three-act lessons, he uses video to pique students' interest in the problem, so after watching the short video, students are asked to make a prediction. Once the students have written a prediction, I move to Act 2.

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Once students have had time to write a prediction, I facilitate a class discussion on what information the students believe they will need to solve this problem. Typically, students quickly realize they will need the distance each person actually travels. What may not come as easily is the information about each person's rate of travel. Once students request these two pieces of information, I reveal it on the smartboard. I then remind them of the initial question and set the timer for 12 minutes. I explain that they should be able to justify their answer with proof and table groups should be ready to present their ideas to the class when the timer sounds.

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Once the work timer sounds, I select table groups to present their findings. After the first group presents, I record their answer on chart paper and ask for another group to come forward. I repeat this procedure, asking clarifying questions as needed, until all the groups have presented. We then watch the Act 3 video which reveals the answer to the students.

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Because this lesson is the final lesson of the Playing Around with Pythagoras unit, I quickly take a learning level poll for each of the major concepts of the unit (solving unknown side lengths of right triangles, estimating lengths of non-perfect square roots, and solving application problems involving Pythagorean Theorem). My students rate their level of learning using a scale from 1 to 5, ( 1= I don't understand at all to 5= I could teach this concept to someone else). I gather this final feedback so that I can adjust the content of the review game I have created for the following day (Day 11) which will give us practice for the formal assessment (Day 12).